When the first high-resolution simulations of cold dark matter halos
became available
[31],
they had a central density profile approximately
(r)
r-1, which has come to be known as
the central "cusp." It was soon pointed out
[32,
33]
that this
central behavior was inconsistent with the HI observations of dwarf
galaxies that were then becoming available, which suggested that the
central density is roughly constant, and also that the first cluster
lensing observations appeared to be inconsistent with a
r-
central cusp with = 1
[32].
Many additional rotation curves of
low surface brightness (LSB) galaxies were measured, and they also
were claimed to imply that the central density of these galaxies is
rather flat. It was subsequently realized that the HI observations of
galaxies were affected by finite resolution ("beam smearing"), and
that when this was taken into account the disagreement with
simulations is alleviated
[34].
More recently, higher resolution
H and CO rotation curves
have been obtained for a few nearby dwarf and low surface brightness
galaxies
[35], and the highest
resolution two-dimensional data imply a variety of central density
profiles ranging from 0 to 1, with evidence
for radial motion especially in the
0 cases
[36].

Meanwhile, theorists have done simulations with improving resolution.
On the basis of simulations with tens of thousands of particles per
dark matter halo, Navarro, Frenk, & White (NFW)
[37] showed that
halos from galaxy to cluster scales have density profiles that are
described fairly well by the fitting function
NFW(r)
s(r /
rs)-1(1 +
r / rs)-2. Subsequently, James Bullock
[38] and Risa Wechsler
[39]
improved our understanding of halo
evolution in their dissertation research with me, which included
analyzing thousands of dark matter halos in a high-resolution
dissipationless cosmological simulation by Anatoly Klypin and Andrey
Kravtsov. Defining the (virial) concentration
cvirRvir / rs (where
Rvir is the virial radius, Bullock et al.
[38]
showed that at fixed halo mass cvir varies with redshift
z as
(1 + z)-1, and developed an approximate mathematical model
that explained the dependence on mass and redshift. (An alternative
model was proposed in
[40],
but it appears to be inconsistent with a recent simulation of small-mass
halos
[41].)
Wechsler et al.
[39]
determined many halo structural merger trees, and showed that the
central scale radius rs is typically set during the
early phase of
a halo's evolution when its mass is growing rapidly, while
cvir
subsequently grows with Rvir during the later slow
mass accretion
phase. Higher resolution simulations with roughly a million particles
per halo gave central density profiles
(r)
r-
with as steep as 1.5
[42],
although more recent very high
resolution simulations are finding less steep central profiles with
1 or shallower as
r 0
[43].
The disagreement between the theoretical
1 - 1.5 vs. the
observed 0 - 1 may just
reflect the effects of baryonic
matter in the centers of galaxies and the difference between circular
velocity and rotation speed likely to arise in gaseous disks embedded
within triaxial halos
[44].

The mean density
V/2
inside the radius rV/2 (where the
rotation velocity reaches half the maximum observed value) appears to
be somewhat smaller than the
CDM prediction with
8 = 0.9, but
more consistent with
CDM with
8 = 0.7 [45]
or "quintessence" models with equation of state parameter w < - 1
[46],
but as we have mentioned these possibilities
appear to be inconsistent with other data (e.g.
[11]).

In several clusters of galaxies, after removing the baryonic
contribution the central dark matter profile appears to be rather
shallow, with 0.35 for cluster
MS2137-23
[46].
The apparent disagreement with CDM worsens if adiabatic compression of the
dark matter by the infalling baryons is considered
[47]. However,
dynamical friction of the dense galaxies moving in the smooth
background of the cluster dark matter counteracts the effect of
adiabatic compression, and can lead to energy transfer from the
galaxies to the dark matter which heats up the central cuspy dark
matter and softens the cusp. N-body simulations
[48]
show that the dark matter distribution can become very shallow, with
0.3 for a cluster
like MS2137, in agreement with observations.
Taking the triaxial shapes of cluster centers
[49]
into account may also help to bring theory and observations into agreement
[50].